The distribution system for the Herman Company consists of three plants, two warehouses, and four customers. Plant capacities and shipping costs per unit (in $) from each plant to each warehouse are as follows:
Plant 1: Capacity = 100 units, Shipping costs to Warehouse 1 = $5, Shipping costs to Warehouse 2 = $7
Plant 2: Capacity = 150 units, Shipping costs to Warehouse 1 = $6, Shipping costs to Warehouse 2 = $8
Plant 3: Capacity = 200 units, Shipping costs to Warehouse 1 = $4, Shipping costs to Warehouse 2 = $6
Customer demand and shipping costs per unit (in $) from each warehouse to each customer are as follows:
Warehouse 1: Customer 1 demand = 50 units, Shipping costs to Customer 1 = $10, Customer 2 demand = 75 units, Shipping costs to Customer 2 = $12
Warehouse 2: Customer 3 demand = 100 units, Shipping costs to Customer 3 = $8, Customer 4 demand = 125 units, Shipping costs to Customer 4 = $10
Choose the correct network representation of this problem.
(i)
(ii)
(iii)
(iv)
Model (ii)
Model (i)
Model (ii)
Model (iii)
Model (iv)
Formulate a linear programming model of the problem. For subtractive or negative numbers, use a minus sign even if there is a + sign before the blank.
Let Xij represent the relation between plants to warehouses or the relation between warehouses to customers.
MIN
X14 + X15 + X24 + X25 + X34 + X35 + X46 + X47 + X48 + X49 + X56 + X57 + X58 + X59
S.T.
1) X14 + X15 < 50
2) X24 + X25 < 75
3) X34 + X35 < 100
4) X46 + X47 + X48 + X49 + X14 + X24 + X34 = 100
5) X56 + X57 + X58 + X59 + X15 + X25 + X35 = 125
6) X46 + X56 = 150
7) X47 + X57 = 100
8) X48 + X58 = 125
9) X49 + X59 = 200
Solve the linear program to determine the optimal shipping plan.
Objective Function Value =
Variable Value Reduced Costs
X14
X15
X24
X25
X34
X35
X46
X47
X48
X49
X56
X57
X58
X59
There is an excess capacity of ??? units at
plant 1
plant 2
plant 3
